Dynamic analysis of a pipe conveying a two-phase fluid considering uncertainties in the flow parameters
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TECHNICAL PAPER
Dynamic analysis of a pipe conveying a two‑phase fluid considering uncertainties in the flow parameters P. J. V. Ponte1 · T. G. Ritto2 · J.‑F. Deü3 Received: 20 August 2020 / Accepted: 15 October 2020 / Published online: 16 November 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract This paper is interested in the dynamics of a horizontal pipe conveying a two-phase fluid (gas and liquid), which is a problem of great regard for the oil and gas industry. The purpose of this paper is twofold. First, it introduces dimensionless coefficients that carry the information of the two-phase flow, allowing the dynamic equation to be written analogously to the equation of a single-phase fluid. Second, a probabilistic model is developed considering uncertainties in three flow parameters, (1) the flow profile factor, (2) the slip ratio and (3) the vapour quality, in order to analyse the influence of these parameters on the dynamic stability and on the frequency response of the system. The pipe is described using the linear elastic Euler–Bernoulli beam theory, and the fluid is modelled taking into account a constant tangential velocity of the flow. The coupled system is discretized by means of the finite element method, and the stochastic problem is approximated using the Monte Carlo method. The flow parameters affect greatly the system response, and different values of the critical flow velocity are obtained, depending on the level of uncertainty of the parameters. Keywords Dynamic instability · Stochastic model · Two-phase flow · Piping vibrations · Dimensionless parameters
1 Introduction Two-phase fluid and high flow velocities are often present in oil production pipes of operational units of the Pre-Salt reservoirs, for which the process requires high values of flow rate and gas-oil ratio [2]. According to the Energy Institute [6], the use of thin-walled pipes and the high flow velocities Technical Editor: Andre T. Beck, Dr. * P. J. V. Ponte [email protected] T. G. Ritto [email protected] J.‑F. Deü jean‑[email protected] 1
PETROBRAS - Petróleo Brasileiro S.A., Av. Henrique Valadares 28, Centro, Rio de Janeiro, RJ 20231‑030, Brazil
2
Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Rua Moniz Aragão 360, Cidade Universitária, Rio de Janeiro, RJ 21941‑594, Brazil
3
Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC) - CNAM, 292 Rue Saint‑Martin, 75003 Paris, France
are considered the most significant factors that contribute to the pipe vibration issues in the oil and gas industry. Thus, it is important to understand the pipe vibration phenomena to avoid environmental hazard and to ensure operational continuity and safety in the production units. In this regard, some researches have shown that over 20% of all hydrocarbon released to the environment in the UK sector of the North Sea come from vibrations and fatigue issues, and in the western Europe around 12% of pipe failures are related to vibrat
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